Final answer:
The probability of drawing 2 red marbles from the jar at the same time is 6/11, which can be approximated as 0.5455.
Step-by-step explanation:
The probability of drawing 2 red marbles at the same time from a jar that contains 3 blue marbles and 9 red marbles can be calculated using combinatorial methods. The total number of ways to draw 2 marbles from the jar is the combination of 12 marbles taken 2 at a time, which is calculated as C(12, 2). The number of ways to draw 2 red marbles is the combination of 9 red marbles taken 2 at a time, which is C(9, 2). The probability is then the ratio of successful outcomes to the total number of outcomes, so P(2 red marbles) = C(9, 2) / C(12, 2).
First, calculate C(12, 2) using the combination formula: C(n, k) = n! / (k!(n-k)!), which gives us C(12, 2) = 12! / (2!(12-2)!) = 66. Next, calculate C(9, 2) in the same way, which gives us C(9, 2) = 9! / (2!(9-2)!) = 36. Finally, the probability P(2 red marbles) = 36 / 66, which simplifies to 6/11 or approximately 0.5455.